FULL TEST – I

Question Paper 23 Pages

Joint Entrance Examination (Main)

Miscellaneous

SRM

Contributed by

Sohail Rao Murthy

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com

FULL TEST – I

Time Allotted: 3 Hours Maximum Marks: 432


Please read the instructions carefully. You are allotted 5 minutes
specifically for this purpose.
 You are not allowed to leave the Examination Hall before the end of
the test.

INSTRUCTIONS

A. General Instructions
1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.
2. This question paper contains Three Parts.
3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.
4. Each part has only one section: Section-A.
5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be
provided for rough work.
6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic
devices, in any form, are not allowed.
B. Filling of OMR Sheet
1. Ensure matching of OMR sheet with the Question paper before you start marking your answers
on OMR sheet.
2. On the OMR sheet, darken the appropriate bubble with black pen for each character of your
Enrolment No. and write your Name, Test Centre and other details at the designated places.
3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts.

(i) Section-A (01 to 03 and 10 to 12) contains 6 multiple choice questions which have only one
correct answer. Each question carries +8 marks for correct answer and – 2 mark for wrong
answer.

Section-A (04 to 09 and 13 to 30) contains 24 multiple choice questions which have only one
correct answer. Each question carries +4 marks for correct answer and – 1 mark for wrong
answer.

Name of the Candidate

Enrolment No.

ALL I
NDIA TEST SERIES

FIITJEE

JEE (Main), 2014

From Classroom/Integrated School Programs
7 in Top 20, 23 in Top 100, 54 in Top 300, 106 in Top 500 All India Ranks & 2314 Students from Classroom
/Integrated School Programs & 3723 Students from All Programs have been Awarded a Rank in JEE (Advanced), 2013

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Useful Data

PHYSICS
Acceleration due to gravity g = 10 m/s
2

Planck constant h = 6.6 10

34
J-s
Charge of electron e = 1.6  10

19
C
Mass of electron m
e
= 9.1  10

31
kg
Permittivity of free space 
0
= 8.85  10

12
C
2
/N-m
2
Density of water 
water
= 10
3
kg/m
3

Atmospheric pressure P
a
= 10
5
N/m
2

Gas constant R = 8.314 J K

1
mol

1
CHEMISTRY

Gas Constant R = 8.314 J K

1
mol

1

= 0.0821 Lit atm K

1
mol

1

= 1.987  2 Cal K

1
mol

1

Avogadro's Number N
a
= 6.023  10
23

Planck’s constant h = 6.625  10

34
Js
= 6.625  10
–27
ergs
1 Faraday = 96500 coulomb
1 calorie = 4.2 joule
1 amu = 1.66  10
–27
kg
1 eV = 1.6  10
–19
J

Atomic No: H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8,
N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16,
Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25,
Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33,
Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56,
Pb=82, U=92.
Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16,
F=19, Na=23, Mg=24, Al = 27, Si=28, P=31, S=32,
Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59,
Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108,
Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238.

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P
P
h
h
y
y
s
s
i
i
c
c
s
s PART – I

SECTION – A

Single Correct Choice Type

This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE is correct.

1. One quarter of the plate is cut from a square plate as shown in the figure. If
‘M’ is the mass of the plate and ‘’ is the length of each side, then the moment
of inertia of the plate about an axis passing through ‘O’ and perpendicular to
the plate is
(A) M
2
/ 8 (B) 3M
2
/4
(C) M
2
/3 (D) 3M
2



O

2. A block is suspended by an ideal spring constant K. If the block is pulled down by constant force
F and if maximum displacement of block from it’s initial position of rest is z, then
(A) z = F/K (B) z = 2F/K
(C) work done by force F is equal to 2Fz.
(D) increase in potential energy of the spring is
2
1
Kz
2

3. A particle starts from rest and moves with an acceleration of a = {2 + |t – 2|} m/s
2
, the velocity of
the particle at t = 4 sec is
(A) 2 m/s (B) 4 m/s
(C) zero (D) 12 m/s.

4. A large tank filled with water of density

and surface tension

is
being siphoned out using a glass capillary tube of cross-sectional
radius r
. If the siphon action starts without any external agent, then
(angle of contact is zero).
(A) H
gr



(B)
2
H
gr




(C)
2
H h
gr

 

(D)
2 2
H h
gr

 


H
h

Space for Rough work
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5. A copper rod and a steel rod of equal cross-sections and
lengths (L) are joined side by side and connected between
two heat baths as shown in the figure. If heat flows through
them from x = 0 to x = 2L at a steady rate, and conductivities
of the metals are K
cu
& K
steel
(K
cu
> K
steel
), then the
temperature varies as: (convection and radiation are
negligible)
X = 0 X = 2L
Cu
Steel
X = L

(A)
T
x = 0
x = 2L

(B)
T
x = 2Lx = L

(C)
T
L
2L
x

(D)

T
L
2L
x

6. A non –conducting rod AB of length l has a total charge q. The rod
is rotated about an axis passing through its center of mass with a
constant angular velocity

as shown in the figure. The magnetic
moment of the rod is
(A)
2
q l
12

(B)
2
q l
3


(C)
2
q l
24

(D)
2
q l
6


A
C
B


Space for Rough work
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7. The figure shows a potentiometer arrangement. D is the driving
cell, C is the cell whose e.m.f. is to be determined. AB is the
potentiometer wire and G is a galvanometer. J is a sliding contact
which can touch any point on AB. Which of the following are
essential conditions for obtaining balance?
(A) The e.m.f. of D must be greater than the e.m.f. of C
(B) The positive terminals of D and C both must be joined to A
D
A
B
J
G
C

(C) The resistance of G must be less than the resistance of AB
(D) None of these

8. Three capacitors each having capacitance C = 2 µF are
connected with a battery of e.m.f. 30 V as shown in the
figure. When the switch S is closed. The amount of charge
flown through the battery is
(A) 20 µC (B) 24 C
(C) 10 C (D) 40 C
30 V
C
C
C
S

9. A conducting rod of length l is hinged at point O. It is free to rotate
in a vertical plane. There exists a uniform magnetic field
B

in
horizontal direction. The rod is released from the position shown in
the figure. The potential difference between the two ends of the
rod when it rotates through an angle  is proportional to:
(A) 
2
(B) 
3/2

(C) sin θ (D) None of these
l

B
O

10. If
a

and
b

are two non parallel vectors then




a a b . a b
 
  
 
 
  
is equal to
(A) a
3
b
2
(B) a
2


a.b



(C) zero (D) None of these

11. A boat goes downstream for half an hour and then goes upstream for half an hour. The total
distance travelled by the boat in the ground frame for this is 20 km. Ii is known that speed of the
boat relative to the river for the whole trip was constant and greater than the speed of the river.
The distance travelled by the boat in the frame of the river for this is
(A) zero (B) 20 km
(C) 10 km (D) can’t be determined
Space for Rough work
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12. A particle of mass m is attached to a rod of length L and it rotates in a circle
with a constant angular velocity . An observer P is rigidly fixed on the rod
at a distance L/2 from the centre. The acceleration of m and the pseudo
force on m from the frame of reference of P must be respectively
(A) zero, zero (B) zero,
2
L
m
2




P
O
m

L

(C)
2
L
2
 ,
2
L
m
2
 (D) zero, m
2
L

13. For a certain organ pipe open at both ends, the successive resonance frequencies are obtained
at 510, 680 and 850 Hz. The velocity of sound in air is 340 m/s. The length of the pipe must be
(A) 2 m (B) 0.5 m
(C) m (D) 0.25 m

14. A short linear object of length 1 mm lies along the axis of a biconvex lens of focal length 5 cm at a
distance of 15 cm. The length of the image will be approximately
(A) 1/16 mm (B) 1/4 mm
(C) 1/2 mm (D) 1/8 mm

15. The left plate of the capacitor shown in the figure above carries a
charge +Q while the right plate is uncharged at t = 0. The total
charge on the right plate after closing the switch will be
(A)
Q
2
+ C (B)
Q
2
 C
(C) 
Q
2
(D)  C


C

+Q

0

16. A small sphere and a big sphere are released from rest with a very small
gap from height h as shown in the figure. The mass of bigger sphere is
very large as compared to mass of smaller sphere the height from the
point of collision of smaller sphere with the bigger sphere to which the
smaller sphere will rise if all the collisions are elastic
(A) 2h (B) 4h
(C) 6h (D) 9h

h

Space for Rough work
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17. The distance between two parallel plates of a capacitor is a. A
conductor of thickness b(b < a) is inserted between the plates
as shown in the figure. The variation of effective capacitance
between the surfaces of conductor and plate as a function of
the distance (x) is best represented by

a
b

x

(A)

(a- b)
C

x

(B)

(a - b)
C

x

(C)

(a
–
b)

C

x

(D)

(a
–
b)

C

x

18. Three blocks A, B and C having masses m kg 2kg and 3 kg are attached by
massless strings and ideal pulleys as shown in the figure. When the system is
released from rest if the block ‘A’ remains stationary , the mass of block ‘A’ is
(A) 2.2 kg (B) 2.6 kg
(C) 2.4 kg (D) 4.8 kg

B
C

A

19. A block of mass 2 kg is attached to one end of a massless rod of length
1
m

. The rod is fixed to
a horizontal plane at the other end such that the block and rod are free to revolve on a horizontal
plane. The coefficient of friction between the block and surface is 0.1. Block is made to rotate
with uniform speed by applying a constant external force in tangential direction on the block. The
work done by external force when the rod rotates by 90
0
is
(A) 0 (B) 10 joule
(C)
joule
2

(D) 1 joule

20. A solid sphere of radius R, and dielectric constant ‘k’ has spherical cavity of radius R/4. A point
charge q
1
is placed in the cavity. Another charge q
2
is placed outside the sphere at a distance of
r from q. Then Coulombic force of interaction between them is found to be ‘F
1
’. When the same
charges are separated by same distance in vacuum then the force of interaction between them is
found to be F
2
then
(A) F
1
= F
2
/k (B) F
2
= F
1
/k
(C) F
1
. F
2
=
1
k
(D) F
1
= F
2

Space for Rough work
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21. A solid cylinder is wrapped with a string and placed on an inclined
plane as shown in the figure. Then the frictional force acting
between cylinder and plane is
(A) zero (B) 5 mg
(C)
7mg
2
(D)
mg
5

60
0

 =0.4

22. The relation between R and r (internal resistance of the battery)
for which the power consumed in the external part of the circuit
is maximum.
(A) R = r (B)
r
R
2


(C) R = 2r (D) R = 1.5 r



R

R

R

R

R

R

4
R

r

23. An equilateral triangular loop having a resistance R and length of each side ‘’ is
placed in a magnetic field which is varying at
dB
dt
= 1 T/s. The induced current
in the loop will be

x x x x

x x x x x x
x x x x x x
x x x x x x
x x x x x x

x x x

(A)
3
4
2
R

(B)
4
3
2
R


(C)
3
4
2
R

(D)
4
3
2
R


24. The temperature of a mono-atomic gas in an uniform container of
length ‘L varies linearly from T
0
to T
L
as shown in the figure. If the
molecular weight of the gas is M
0
, then the time taken by a wave
pulse in travelling from end A to end B is

A B
T
L
T
0
L

(A)
L 0
2L 3M
5R
( T T )
(B)
L 0
0
3(T T )
5RM L


(C)
L 0
2L 3M
5R
( T T )
(D) L
0
L 0
M
2R(T T )


Space for Rough work
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25. In the given circuit the reading of ideal voltmeter is E/2.
The internal resistance of the battery is
(A)
1

(B)
2
3


(C)
2
5

(D)
5
2


r
E
2
1
V
E

26. The specific heat capacity of a monoatomic gas for the process TV
2
= constant is (where R is gas
constant)
(A)
R
2
(B) 2R
(C)
R
3
(D)
R
4

27. 12 identical rods made of same material are arranged in the
form of a cube. The temperature of ‘P’ and ‘R’ are maintained
at 90
0
C and 30
0
C respectively. Then the temperature of
point ‘V’, when steady state is reached,
(A) 65C (B) 60C
(C) 20C (D) 50C

T

U

S

R

V

W

a

30
0
C
90
0
C
Q

P

28. A block is placed at the the bottom of an inclined plane and slided
upwards with some initial speed. It slides up the incline, stops after
time t
1
, and slides back in a further time t
2
. The angle of inclination
of the plane with the horizontal is θ and the coefficient of friction is
. Then
(A) t
1
> t
2
(B)

t
1
< t
2




(C) t
1
= t
2
(D) t
1
= t
2
only if θ
4



29. A projectile is thrown from the base of an inclined plane at an angle 45°
with the plane. At what angle may it hit the plane again?
(A) 30° (B) 45°
(C) 60° (D) all of the above.
45°

30. In an artificial satellite which of the following process of heat transfer will not take place?
(A) Conduction (B) Convection
(C) Radiation (D) All of the above

Space for rough work

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C
C
h
h
e
e
m
m
i
i
s
s
t
t
r
r
y
y PART – II

SECTION – A
Straight Objective Type

This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices (A),
(B), (C) and (D), out of which ONLY ONE is correct.

1. Which one of the following is correct?
(A) If one component of a binary liquid-liquid solution deviate negatively from Raoult’s law, then
the solution will form minimum boiling point azeotrope.
(B) for a solution of two liquids (A and B), V
sol
> V
A
+ V
B
; then A and B can be separated by
fractional distillation.
(C) Deep sea divers use a mixture of He and O
2
instead of air due to less solubility of He in blood
in comparison to N
2
, which cause the bends, i.e. pain due to bubbling of untreated gas
dissolved in blood.
(D) All of the above.

2. A compound is composed of two elements A and B, element A constitute f.c.c. lattice, while B
occupy all the tetrahedral voids, in this way another simple cubic is constituted by element B,
inside the fcc unit cell of element A. If all the points/particles along any one edge of inner cube of
every unit cell, are missing then what is the new empirical formula of the compound
(A) A
4
B
6
(B) A
2
B
8

(C) A
2
B
3
(D) AB
4

3. Which of the following gives yellow precipitate with aq. AgNO
3
?
(A) KIO
3
(B) KI
(C) CHI
3
(D) CH
2
I
2

4. How many planes of symmetry and axis of symmetry are there in one molecule of PCl
3
F
2
,
respectively?
(A) 4, 7 (B) 7, 13
(C) 7, 10 (D) 4, 10

5. Two cylinders A and B of equal volumes are filled and equal masses of N
2
and O
2
, respectively.
Cylinder A is kept at 300 K while B is kept at 600 K, then (assume ideal behaviour of both gases)
(A) Average kinetic energy of N
2
(per mole) in A is equal to that of O
2
in B.
(B) Molecules in cylinder B move twice as fast as those in A.
(C) Pressure in flask A is less than that of B.
(D) Average velocity of N
2
is equal to rms velocity of O
2
, in the given conditions.
Space for Rough work

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FULL TEST – I

FULL TEST – I

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